answers-02-03-2011 - Answers to Physics 176 One-Minute...

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Unformatted text preview: Answers to Physics 176 One-Minute Questionnaires Lecture date: February 3, 2011 What motivated entropy? I don’t know the history well (few scientists take the time to learn historical details, including myself) and my comments below should be taken with a grain of salt. Take a look at the Wikipedia article “Entropy” and also look through Chapter 4 of Schroeder, which summarizes the traditional thermo- dynamics approach to entropy via heat engines and refrigerators. There are also many books, popular and technical, that discuss the history, and some of these are listed at the back of Schroeder (e.g., the book “The Second Law” by P. Atkins). My understanding is that much of the motivation for thinking about entropy was driven by the practical needs of the industrial revolution, by people who wanted to replace animals and people with machines such as water wheels and steam engines. Builders of steam engines and scientists (which were sometimes the same person) started trying to figure out em- pirically and conceptually how well could one do in converting energy from fuel, say burning wood, to getting useful work out of a machine. Over time, scientists realized (and it is here that I don’t know the history) that an im- portant quantity for understanding steam engines was the ratio Q/T , heat Q exchanged between two systems divided by some temperature T , either the temperature of the system receiving the heat or the system giving up the heat, and this ratio was called “entropy”. It was discovered empirically that entropy always increased, which prevented perfectly efficient machines from existing, and also discovered theoretically that entropy set hard limits on the efficiency of engines, as you saw a little bit in the recent homework problem (Problem 4.1 in Schroeder). Toward the end of the 19th century, several decades after the entropy was identified as Q/T , scientists like Boltzmann developed a new understanding of entropy by using kinetic theory to interpret heat in terms of microscopic details. This led to Boltzmann’s great discovery (also one of the highlights of this course), that the thermodynamic entropy could be understood as count- ing possible microstates of specified macrostates, S = k ln(Ω). (Boltzmann was so proud of this insight that he asked that this formula be engraved on his tomb in Vienna after his death.) But Boltzmann’s insight was limited by the inability of classical mechanics to identify correctly what was a mi- crostate as shown by the wrong predictions of the equipartition theorem. It was not until the invention of quantum mechanics in the 1920s that a defini- 1 tive understanding of “microstate” was achieved and then entropy became a clear valuable concept that could be used quantitatively and unambiguously in all areas of science....
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answers-02-03-2011 - Answers to Physics 176 One-Minute...

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